Decays χcJ(J=0,1,2)→ωφ are studied using (448.1±2.9)×106ψ(3686) events collected with the BESIII detector in 2009 and 2012. In addition to the previously established χc0→ωφ, the first observation of χc1→ωφ is reported in this paper. The measured product branching fractions are B(ψ(3686)→γχc0)×B(χc0→ωφ)=(13.83±0.70±1.01)×10-6 and B(ψ(3686)→γχc1)×B(χc1→ωφ)=(2.67±0.31±0.27)×10-6, and the absolute branching fractions are B(χc0→ωφ)=(13.84±0.70±1.08)×10-5 and B(χc1→ωφ)=(2.80±0.32±0.30)×10-5. We also find strong evidence for χc2→ωφ with a statistical significance of 4.8σ, and the corresponding product and absolute branching fractions are measured to be B(ψ(3686)→γχc2)×B(χc2→ωφ)=(0.91±0.23±0.12)×10-6 and B(χc2→ωφ)=(1.00±0.25±0.14)×10-5. Here, the first errors are statistical and the second ones systematic.